This invention relates generally to a digital alarm wristwatch with an electro-optical display device. In conventional electronic alarm wristwatches, the alarm buzzer is positioned in the back side of the watch below the digital display. The alarm sound is released from the back of the watch case so that the sound is interrupted by the wearer's wrist. As an electronic alarm wristwatch is driven by a small button-type battery, sufficient sound cannot be obtained by conventional placement of the alarm buzzer in the back side of the watch below the display device. When holes are provided for releasing the alarm sound on the back side, they may not be provided on the flat portion, but must be placed on a slanted portion of the case back in order to prevent interruption of sound by the wearer's wrist. When a cover for the battery is also provided, the case back becomes very complicated. This arrangement frequently results in the display panel, buzzer and battery overlapping each other, which results in a thick wristwatch.